Congress passed a law that established the fee in the early 1980s, to be paid by customers who use electricity from reactors. But soon after President Obama took office, he made good on a campaign promise and stopped work on the disposal site selected by Congress, Yucca Mountain, about 100 miles from Las Vegas.

The fund so far has spent about $7 billion, mostly on Yucca, and has about $30 billion on hand, including interest income.

The energy secretary is supposed to set the level of the fee based on the costs of the program, and the department had argued that for the purposes of calculation,...